In this paper we present a novel slanted-plane model which reasons jointly about occlusion boundaries as well as depth. We formulate the problem as one of inference in a hybrid MRF composed of both continuous (i.e., slanted 3D planes) and discrete (i.e., occlusion boundaries) random variables. This allows us to define potentials encoding the ownership of the pixels that compose the boundary between segments, as well as potentials encoding which junctions are physically possible. Our approach outperforms the state-of-the-art on Middlebury high resolution imagery [1] as well as in the more challenging KITTI dataset [2], while being more efficient than existing slanted plane MRF methods, taking on average 2 minutes to perform inference on high resolution imagery.